DeMaurice Smith, the executive director of the NFL Players Association, ran for his post in early 2009 emphasizing his Washington, D.C., connections and the ability to affect—through politics—the union’s relationship with the NFL.

Smith, a former lawyer with Patton Boggs, has stayed true to his word, organizing delegations of players to visit Capitol Hill, threatening to make an issue of the NFL’s antitrust exemption for broadcast contracts and getting the AFL-CIO to lobby NFL owners.

“I don’t understand it,” said Bill Gould, a former National Labor Relations Board chairman under President Bill Clinton and currently a Stanford law professor. “I just don’t see where it’s going.”

The two congressional-mandated possibilities to help settle the labor impasse, Gould said, would be to remove the antitrust exemption or impose compulsory arbitration. That seems highly unlikely given the new Republican majority in the House.

New House Judiciary Chairman Lamar Smith, R-Texas, said earlier this month as players were visiting Capitol Hill, “That is a business dispute. The owners and players are both literally and figuratively big boys and do not need Congress to referee every dispute for them.”

Jeff Miller, the NFL’s senior vice president for government affairs, agreed that Congress should not be involved, though the league remains active on the Hill. He said the league would meet with all members of Congress visited by the NFLPA, and described the league’s role as reactive.

The NFLPA could not be reached for this story, but has cited publicly the NFL’s political action committee and campaign contributions as evidence that the union needs a stronger presence on Capitol Hill.